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I commented on Ben/Rob's 538 article just after it came out and wrote up a brief article for my web site: https://t.co/4DNVkX9pNJ. I concluded that the increase in HR/contact was completely consistent with a small (~1 mph) increase in average exit speed. I have been meaning to extend the analysis into the 2016 season but haven't completed it yet.
Thanks. Changing ln(T) by 1 is a change from 90F to 33F, which is a big change. You find a change in exit velocity by ~1 mph. The best I can do is estimate based on the change in COR of the ball, which changes by about 5.7% based on the measurements we did (you can read about it in the last section of this paper: http://baseball.physics.illinois.edu/AJP-June2011.pdf). The corresponding change in exit velocity is about 3.5 mph, which is quite a bit larger than what you found from the statistical analysis.
Of course, for the measurements we did, the baseball had been stored in a constant temperature environment for ~2 weeks, so that we can be pretty sure the temperature was the same throughout the volume of the ball. While it doesn't take 2 weeks to reach temperature equilibrium, it probably takes a lot longer than just a few hours, so it is not so surprising that you find a smaller effect.
I have learned a lot from your analysis. Still trying to learn more.
I have a question regarding the temperature term in the exit velocity model. Is there an easy way to summarize what you found for that term? Or specifically, what is the effect of temperature on exit velocity? Some effect is expected, since the coefficient of restitution of the baseball is temperature dependent. That effect has been measured and is known reasonably well. It would be interesting to see whether that dependence could account for what you find in your analysis.
That really is an interesting question. It is quite likely that missing data are geometry-dependent, having to do with the location and orientation of the Trackman device. These things are surely park dependent. So, it could be the case that some of the park effects could be due to the missing data. But that is just speculation on my part.
Thanks, Jonathan. I'm still trying to wrap my brain around the park effects associated with Trackman. I have asked the brain trust at Trackman for their thoughts on the subject. Will let you know what they tell me.
Do the park effects in 2016 correlate with those in 2015. If you do random split season for 2015, how do park effects correlate? Or 1st half/2nd half split?
Bryan...regarding you 3rd point, I am suggesting that you not use distance, since it is sort of redundant with exit speed. That is, it's not really new information. And, as I said, it is not actually measured with HitTrax.
Do you know how many MLB players are using this bat? If I recall, <span class="playerdef"><a href="http://www.baseballprospectus.com/card/card.php?id=45464">Dustin Pedroia</a></span>.
I am very fond of doing experiments under controlled conditions (having spent a career doing such things in my own field). This was a very nice study.
Nice work, guys. Regarding the claim of "more efficient power transfer", there are two ways to interpret that. One if more efficient power transfer from bat to ball. Two is more efficient power transfer from batter to bat. I suspect they mean the latter, which is probably similar to the claim of higher bat speed. I can think of no scientific reason why the first interpretation would be the case,and it would be very easy to show that in a laboratory experiment at Washington State.
Why not hit off a tee, thereby removing one extra degree of variability. I guess I am skeptical of the claim of higher bat speed except perhaps as a long term effect due to greater comfort, less chance of hamate injury, etc.
I am curious about your looking separately at exit speed and distance. With HitTrax, distance is a calculated quantity based on exit speed (and launch angle).
Once again, very nice experiment and analysis.
WOW! That's the best interview with a ballplayer I have ever heard! The physics and analytics of baseball PLUS gravitational waves from black hole collisions, all in one podcast.
Actually you are off by a factor of pi (not 2*pi), so that surface speed at 1500 rpm is about 13 mph.
Just for the record, the circumference of the ball is 9", not the diameter. So, your speed numbers are too large by a factor of 2*pi. That is, the surface speed of a ball rotating at 1500 rpm is 6.4 mph, not 40 mph.
Also, as you point out, skin drag is totally unimportant for a baseball moving at typical game speeds, where the Reynold's number is of order 1-2 x 10^5. Form drag completely dominates (drag~square of velocity). Pitch-tracking data from PITCHf/x are consistent with this the quadratic dependence of drag on velocity.
No one has yet computed the motion of a spinning baseball through the air from first principles. So one relies instead on a phenomenological model for the drag and Magnus force to parameterize the dependence on spin and velocity, with unknown "fudge factors" lumped into lift and drag coefficients. In such a model, the Magnus force is proportional to the vector cross product of spin and velocity, which vanishes when the spin is parallel/antiparallel to the velocity. Therefore only the component of spin perpendicular to the velocity result in a Magnus force, hence movement. This is the "transverse" or "movement" spin. The component of spin parallel to the velocity (the "gyrospin") does not lead to movement, since the vector cross product vanishes. The total spin is the Pythagorean sum of the transverse and gyrospin. Trackman measures the total; the transverse part is inferred from the movement. The relationship between the transverse spin and the movement needs to be separately determined in controlled experiments in the laboratory. This has been done at speeds and spins typical of the game, although the relationship is not so well know for very high spins.
Gordon: Knuckleballs have almost no spin and do not fall into either category. Their movement is not the result of the Magnus force.
Schlicht: I'm not sure I follow your point. The line is not the result of a regression analysis. It is simply the line equating the transverse to the total spin. The observation is that for the fastballs, sinkers, changeups, and splitters, the points are scattered randomly about the line. The distribution of differences between the line and the points is plotted in Fig. 2. Now, if you are saying that Fig. 2 should be plotted for each pitch type separately, I can agree that would be a good thing to show (except for the splitters, since there are too few to be meaningful). The others all have a distribution looking more or less like Fig. 2, with close to 0 mean.
Am I addressing your concern?
Randy: Thanks. You raise an interesting point. Let me give you an alternate point of view. What could be more different from a 4S fastball that is "straight" than a pitch that has considerable drop (i.e., a curveball with topspin)? The more topspin, the more drop. Is it possible for a pitcher to increase the topspin while maintaining the same total spin (i.e., turning more of the gyrospin into topspin)? I don't know the answer. But my gut feeling is that if a pitcher can control the spin axis in that manner, that would be a good thing. If nothing else, it would be another tool in the pitcher's arsenal.
BTW, nice simple derivation of the so-called "barometric formula" relating pressure (or air density) to elevation can be found here (assuming constant temperature): http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/barfor.html.
tsweber: I'm sorry but I just don't agree with you. Here is one reference: http://www2.engr.arizona.edu/~sysengr/publishedPapers/AirDensity.pdf (eq. 8,9). A web search will find many other references. All the references I have consulted have air density decreasing exponentially as a function of elevation. It is also predicted by statistical mechanics and the kinetic theory of gases. If exponential, then clearly nonlinear, but with decreasing (not increasing) rate at higher elevations.
I'd be happy to continue this discussion privately over e-mail (email@example.com).
tsweber: I disagree with your comment and the numbers on air density. I have air density proportional to exp(-elev*beta), with elev in ft and beta=3.709e-5. The derivative wrt elev is largest when elev=0, so a change of 1000 ft at sea level is greater than a change of 1000 ft at 1 mile above sea level. Specifically, I find a change of 0.043 kg/m^3 between 0 and 1000 and 0.036 kg/m^3 between 5280 and 6280.
Commenting more generally on Dan's article: For sure there is less movement to the curveball at higher elevation. However, I would also expect less movement to the slider, for exactly the same reason. On the other hand, there is more "sink" to a sinkerball at the higher elevation. So if I were advising the Rockies, I would load up on sinkerball pitchers. If instead they have loaded up on pitchers who throw sliders, then I must be missing something.
I heard that game on the radio from my hometown in Maine.
No correlation of the type you asked about. Re your other point, that too would be interesting (but not in the scope of our study).
Interesting question, and one that I posed to people I know at Rawlings. Unfortunately, no answer from them.
The drag properties of a baseball are affected by small changes to the surface, such as mud, rosin, pine tar, etc. We did not specifically study these effects in our experiment. But the fact that seemingly identical looking baseballs carry differently suggests that it is true.
Bryan: We measured the weight, diameter, and seam height of each ball. The MLB balls were quite uniform and there was nothing in the physical appearance that gave a clue to their preformance.
MGL: Two different boxes (one dozen each, both boxes previously unopened). Correct, not rubbed with mud. I think the mud does make a difference. But I am not sure if it increases or decreases the uniformity. I can easily convince myself either way. I think the mud roughens the surface, which ought to reduce both the drag and lift (all other things equal). But I don't know how uniformly the ball is rubbed. Good question and something we ought to investigate.
Right! I didn't mean to suggest otherwise.
The size of the Fourier transform has to be a power of 2 if the usual algorithm is used.
The speed of the pitch plays a very small role in determining the speed of the batted ball (attendees of @saberseminar last weekend might recall my mentioning that in my talk). So I doubt there is much correlation between the frequency spectrum and the pitch speed.
I should point out that there is a bit of controversy regarding the origin of the lower-frequency sound for balls hit off the sweet spot. One theory is the one I told Rob, which has to do with the longer collision time. But another, and the one Adair subscribes to, is due to the excitation of low-frequency bending vibrations in the bat (see also my saberseminar talk, which I will shortly post at my web site). It might well be that it is a combination of both effects. Data such as those taken by Rob might help clarify this issue. Or it might be better to take data under more controlled conditions, as in a laboratory.
Other interesting links:
http://baseball.physics.illinois.edu/glanz-nytimes.htm (Jim Glanz of NYT, regarding Adair's article). See also http://baseball.physics.illinois.edu/glanz-crack.jpg
For some reason, the link to the full Adair article seems to be broken (although it wasn't last week when I told Rob about it). Maybe the site is temporarily down. Here it is:
Dan Russell is an acoustical physicist who has compared wood with aluminum:
Re: "...throwing 100+MPH from the outfield is nothing special...". I don't necessarily doubt what you are saying. Just wondering how you know that. In particular, do you have access to data that show that this is the case?
My student, Eric Lang, is busy working on a similar analysis for other great throws (especially the ones pointed out by Rob Neyer last week in his article). If we are successful in obtaining good video, we should be able to do the same type of analysis we did on Cespedes. Then we can compare release speeds, etc.
Update: I have updated my estimates based on new information I have found (courtesy of Eli Baldrige of ESPN Sports Science). Following his advice, I have used the Distance Measurement Tool with (old) Google Maps to come up with a much better distance, D=300 ft. I had earlier found some incorrect info on the web about the distance to the foul plot, which is actually 330 ft. Also, I now have a real-time video that allows me to time the throw by counting frames, with 30 frames/sec. I find that the hang time T=2.80 sec. The longer time I had used earlier was found from a replay that had actually been slowed down.
So, with D-300, T=2.80, I find initial speed=101.5 mph, launch angle=10.0 degrees. The answer is not all that different from before, but I wanted to get the whole thing right. I have posted a new plot of the trajectory on my web site.
"If good hitters always hit, and Mookie Betts has always hit, Mookie Betts is a good hitter."
You realize, I hope, of the logical flaw in that statement.
Excellent article. However, I should correct something you wrote: "Both pitchers’ knuckleballs have an average horizontal (and vertical) movement near zero, which makes sense. PITCHf/x measures movement relative to a “spinless” pitch, and the true knuckleball is thrown virtually without spin.". That statement is not correct. The reason for the movement averaging to zero (in both horizontal and vertical directions) is because the movement is random in direction. It is not because the movement is inherently small. PITCHf/x does not measure spin; it measures movement. For "normal" pitches, the spin is inferred from the movement. That doesn't work for knuckleballs, for which the movement has nothing to do with spin.
All measurements were from the back apex of home plate. In the article I speculate that the slight 0.6 ft offset might be due to a slight shift of origins. The Trackman origin is at the same place, but there is probably some uncertainty in the location where Trackman first picks up the ball. We probably could have figured that out with sufficient time using the device, but it really was a secondary goal for the experiment.
I wonder if any MLB teams have done their own studies of this type. If I were a team that had Trackman installed, I certainly would want to know everything about it.
In cricket, the principal effect is the surface roughness the ball. Typically, the bowler "polishes" one hemisphere during the course of the game to keep it smooth, while the other half is rough (and perhaps gets rougher). That can have a dramatic effect on the "swing" (cricket-speak for movement) of the ball, often resulting in reverse swing. The latter refers to movement in the opposite direction that is expected based on the seam orientation.
Having said all that, I don't know if the shape effect under discussion starts to be more important as the game wears on.
That's an interesting question that no one has ever investigated, to my knowledge. I'm not even sure anyone has even asked the question before. So good for you for asking it. Certainly if the ball changes shape, that will affect the aerodynamic forces of drag and lift and therefore affect the landing point. I don't think it would affect the Trackman comparisons but it would have an effect on the main goal of the experiment, which was to address why the initial velocity vector does not better determine the landing point.
What I can say is that high-speed video of the ball coming off the bat shows that, while the ball really flattens out during contact, it recovers its usual shape pretty much as soon as it leaves the bat. So my gut-level reaction is that the shape is not an issue. But as I said, an interesting question...and worth thinking about. And we will!
Excellent article, Ben. You nailed it!
Zach...I'd like to discuss some of your analysis with you privately. Would you contact me (firstname.lastname@example.org). Thanks.
See the link I just posted: http://baseball.physics.illinois.edu/trackman/SpinAxis.pdf.
Good question, Dan.
Just to clarify, TrackMan does not measure the "true spin axis". It is determined from the measured movement of the pitch, just like it is done with PITCHf/x. However, it does measure the true rate of spin (rpm's), unlike PITCHf/x. I wrote an article about the spin axis for my web site a couple of years ago: http://baseball.physics.illinois.edu/trackman/SpinAxis.pdf
So let's see if I understand: In Colin's table showing LWTS and STDERR, the STDERR is the standard deviation found from the variation (appropriately weighted perhaps?) among the 24 states contributing to the total. If he had used RE24, then there would be no variance (other than the tiny variance in the actual RE24 numbers, which are based on many contributing events and are therefore small). Am I getting it?
I didn't have time to read all the comments, so please excuse me if this has been discussed already. When comparing BRAA for two players, say Trout and Miggy, you have simply added the variances of the two players, then taken the sqrt to get the standard error in their difference. That would be a correct procedure if the variances of the two players are uncorrelated. But are they uncorrelated? I claim no, since they are derived from the same linear weights table. What say you about that?
Very thoughtful article. I particularly like the Chesterton's Fence principle. Without having heard of it before, I actually try to apply it to my own research, particularly in areas where perception and reality do not agree. For me, it is important to understand in such cases not only that perception does not agree with reality but to also understand how the incorrect perception arises. As a recent example, I am currently applying the principle to my study of knuckleball trajectories, trying to understand how they actually behave and what leads to the perception that they behave differently.
Doug...I look forward to hearing your talk at the saberseminar in a couple of weeks.
That subterranean particle accelerator at the Trop was probably installed so that Josh Kalk could keep up with his former life as a high-energy physicist. Josh...if you're listening: How about we do an experiment together, along with Ike Hall, John Walsh, Jeremy Williams, ... (am I missing anyone?).
So tell us what it tells you. Otherwise, I don't see the point of your comment. I'm not trying to be nasty here, just want to know what conclusion about pitch selections (the topic of the article) you draw from Kershaw's ERA at Coors.
I would expect a 4S fastball to be more of a baseline trajectory for a batter, in part because a batter typically sees more of these pitches than any other. Relative to the 4S, a ball thrown with a lot less backspin (SI or splitter) or with topspin (CU) sinks and one thrown with a little extra backspin rises.
I have always speculated that a sinker would be more effective at Coors than elsewhere, at least from a "sink" point of view. As the data shows, the vertical movement on a sinker is upward, so I would expect less upward movement at Coors, meaning more sink. Of course, there will also be less armside movement. Have you taken a look at sinkerball movement at Coors compared to other places?
Responding to some of the questions:
Travis, 1st point: Yes, what you say is true and that adds to the effect of more movement later than earlier in the trajectory. To a good approximation, the force on a spinning baseball is proportional to velocity (v). The flight time is proportional to 1/v. So, deflection is proportional to 1/v. As the ball slows down, you get more deflection.
Travis, 2nd point: The dependence of the air drag on rotation rate is not well established experimentally, although it is a known effect for golf balls. The latest data I have seen for baseballs do not show much of an effect.
kmg1016: See my answer to Travis. Thanks for pointing out the NYT piece. The video presentation they put together is pretty fantastic.
I don't think any of the stuff I just described (slowing down, spin-dependent drag) plays any appreciable role in the question of "late break". The PITCHf/x data tell us that the ball follows very closely to a parabolic trajectory. That is an experimental fact. That necessarily means the break is continuous, with about 67% of it coming in the last 20 ft. I won't quibble about whether the 67% might really be 70% due to these other factors.
Unfortunately, I too missed Graham's presentation. My primary complaint about the conference was the organization of the research talks into parallel sessions. So I could only hear half of them. That is very unfortunate, since hearing the research talks is my primary reason for going to the conference (and paying a rather stiff registration fee). I would be curious to hear the opinion of others on this particular subject.
Nice article. Is there a summary somewhere about what transpired at the visual tracking data panel?
Ah, I misunderstood your original question. In the article, I speculated that the drag increases with backspin. If that really is true, then the drag almost surely increases with the total spin, which is Pythag sum of sidespin and backspin. I did not fully investigate this dependence (but will). What I can say is that, generally speaking, the backspin is much larger than the sidespin, so the total spin is probably only a little larger than the backspin.
Good question. Certainly, the validity of the analysis depends on the accuracy of the data, including the landing point, hang time, and initial velocity vector. I will defer to Greg R. on the landing point and hang time data, since I got that information from him. I suspect the HITf/x data is good to about 1-2 mph, corresponding to a variation of distance by 5-10 ft, which is much smaller that what is observed.
Side spin should not affect the distance in any serious way. It does affect the hook/slice, which affects the spray angle of the landing point. But it has only a small effect on the distance of the landing point from home plate.
What matters for the drag is primarily the density of the air. Viscosity does not directly play a role. The way I like to think about it is that the ball collides with many air molecules, losing a little bit of energy with each collision as it transfers energy to the molecule. When you work out the details, you find that it is the mass density of the air that matters. The air density depends on temperature, elevation, pressure, and relative humidity. The dependence on relative humidity is very small. You can investigate these things for yourself with my "trajectory calculator", http://webusers.npl.illinois.edu/~a-nathan/pob/trajectory-calculator.html. In my analysis, I restricted the home runs I looked at to those with an air density only within +/-2% of a nominal value.
Note: As you said, a higher relative humidity reduces the drag, since a heavier air (nitrogen) molecule is displaced by a ligher water molecule (therefore, lower density).
In MLB, the balls are all "fresh". I am pretty sure any ball that has hit either a bat or the dirt is removed from the game.
Actually, this is a topic that I have investigated experimentally. An account (albeit a technical one from an academic journal) can be found in a paper I wrote last year:
http://webusers.npl.illinois.edu/~a-nathan/pob/ProcediaEngineering34Spin.pdf. I also talked about this topic at the 2010 PITCHf/x summit. You can see a video of the talk here: http://baseball.sportvision.com/summit/archive/2010 (click on my name in the right sidebar).
But here's the bottom line, surprising as it may be:
The spin of a batted ball depends very little on the spin of the pitched ball.
Someday when I get more time, I'll try to put together a less technical article and one more in the style of BPro.
Excellent point. Certainly it is true that the ball really gets mashed when colliding with the ball. And although the ball recovers to its spherical shape shortly after leaving the bat, the resulting damage to the surface of the ball may have an effect on its aerodynamics. But I suspect that is not what is actually happening, given that we see a similar effect with pitched baseballs. My PITCHf/x summit talk from 2011, when I talked about variation in Cd for pitched balls, can be found here: http://webusers.npl.illinois.edu/~a-nathan/pob//ppt/NathanBattedBallAnalysis.ppt, with the relevant stuff on slides 31-35.
Actually I think it has more to do with variation in the surface roughness rather than the seams. There is some additional evidence for ball to ball variation in drag from pitchf/x and TrackMan data on pitched balls. I discussed this briefly at the 2011 pfx summit. The research is still in progress but it might be a good topic for a future article.
Sam...don't give up so easily. How did you estimate the hang time?
I'm a bit skeptical of the claim that this ball was hit very hard. I have a scenario whereby the ball travels 260 with a hang time of 2.55 sec and a maximum height of about 20 ft. The ball is hit with an initial speed of a modest 93 mph at a launch angle of 12 deg. A ball hit that hard at a more optimum launch angle of 30 deg, the ball would have traveled about 350 ft, which is not all that impressive. Had the ball been hit at 110 mph (which would be quite hard) at a launch angle of 6.5 deg, it would have traveled 260 ft in 2.05 sec, reaching a maximum height of about 12 ft. What seems to rule out such a high batted ball speed is the 2.55 sec hang time.
You can look at Greg's home run data to map out the distribution of fly ball distances relative to the fence (i.e., distance between landing point and nearest fence). Then extrapolate that distribution to negative numbers (i.e., fly balls that didn't make it over the fence). When I looked at this distribution across all of MLB stadiums, I found that a 1% change in fly ball distance was equivalent to a ~10% change in home run probability. You can apply that same kind of reasoning to the fence location. That is, move the fence in so that it is 1% closer and you will increase home runs by 10%. It might be interesting to compare that result, given the new fence distance, with your estimate.
There is yet another way to approach this problem, using Greg Rybarczyk's home run records. Greg records the landing point of each home run as well as the height and distance to the nearest fence. One can use those data to estimate the effect of moving the fence in or lowering its height. Strictly speaking, this technique can only be used to investigate moving the fences out, in which case one then asks how many home runs stay in the park. But for small changes, I suspect one can get a good estimate of the effect of moving them in also. One looks at the distribution of fly ball distances and extrapolates inside the current fence position. This is exactly the technique I used to estimate the reduction in home runs expected at Chase Field if they stored the balls in a humidor.
Similar suggestion for movement...limit to one decimal place. Data are not precise enough to justify more.
OK, maybe I am seeing what you are saying. You are saying that the tracking distance is the last 5-6 ft or so, in which case I agree with your numbers. However, I now have to think more carefully about your basic premise that the batter's perception of the pitch speed comes from the last 5 ft or so, when the angular velocity is largest.
Sorry...insert "inch" after the 1/2 on the second line of my comment.
Matt...excellent article, as usual.
I get the essence of what you are saying. However, I am having some problems with the numbers. You say that a 1 mph difference in pitch speed amounts to a 1/2 in difference in tracking distance. Suppose we have a 90 mph pitch (average speed) traveling over, say, 50 ft., so that the flight time is 0.379 sec. If the pitch speed is increased to 91 mph, the pitch will cover 50.6 ft in the same amount of time (0.379 sec). The difference is 0.6 ft or 7", not 1/2". A difference of 3.5" is only a 1/2 mph difference in equivalent pitch speed. Perhaps I am misunderstanding what you are saying, in which case I might be missing the whole point of the paper. Help me out!
I would bet instead on Kalish to AAA (as Ross is activated). Then Nava in LF, Ross in CF, DMac in RF (assuming Pods is unavailble).
As I said earlier, I regard the spin determined from PITCHf/x to be "pseudospin". It is the spin derived from the movement. I believe the movement that PITCHf/x determines. To use that to determine the pseudospin requires some relationship between movement and spin. I talk about that in the article I referred to earlier. The relationship is known only to about +/-20%. Even if it were known perfectly, this technique only determines the "transverse" spin (i.e., the components of spin perpendicular to the direction of motion). The component along the direction of motion (the "gyro" component) is not determined. I question the value of the latter. I am not saying it is not valuable. I am only saying that its value has not yet been demonstrated to me.
One more point: I wrote a little article last year for my web site on using the combination of movement and TrackMan spin to obtain the spin axis. It's a bit technical. But for what it's worth, here's the link:
See my new comment below. I had always thought that there is more value in the "pseudo-spin" inferred from the movement. You have said that your MLB contact says there is more value in the total spin (from Trackman, presumably). Hard to argue with someone who has all the data (and I don't).
The other system is probably TrackMan, which measures the total spin (including any gyro component). The TrackMan people have argued that the total spin is well correlated with swing-and-miss rate for curveballs (see http://sportsillustrated.cnn.com/2011/writers/tom_verducci/04/12/fastballs.trackman/index.html). The comment of your front-office contact that there is more value in the total spin than in the "pseudo-spin" measured by PITCHf/x is very intersting. It would be nice to see the analysis that shows that, but unfortunately the TrackMan data are not publicly available.
And just to clarify my comment about the spin not being measured: It is inferred from the movement, not directly measured. A model is used to make the association between spin and movement. No "gyro" component of the spin is determined from this technique. Whether or not a gyro component is a useful piece of information has yet to be determined (at least not by anyone who is willing to talk about it).
"There's absolutely more to a fastball, or any pitch, that what's captured by Pitchf/x."
Not much more. The actual spin is not measured nor is the actual release point. Everything else you would ever want to know about the pitch IS measured (i.e., the full trajectory). The trick is finding the right way to look at the data from a scouting point of view.
A pitch that has a lot of vertical movement necessarily has a lot of spin. It is the backspin that leads to the vertical movement. So, I am puzzled that you see a correlation with vertical movement but none with spin.
Now, I will admit that vertical movment is more likely to lead to swing-and-miss than horizontal movement, given the dimensions of the bat and ball.
Just so everyone knows, the somewhat anonymous writer of the previous comment is Ed Frank, who is probably known to attendees of the annual PITCHf/x summit (he has been at the last three). The "view from above" of the trajectory is certainly odd, as Ed points out. The horizontal coordinate is the PITCHf/x "x", so that positive/negative numbers are in the direction of a left/right-handed hitters, respectively. So, for this to be a "view from above", the trajectories should all be reflected about the horizontal axis. Sorry if my plot caused confusion.
It is the unpredictability of the trajectory that makes it difficult to hit or catch. Ordinary pitches almost certainly do not flutter. Rather, the small deviations for those pitches from the smooth curve is simply random measurement error. The surprise (at least to me) was that knuckleballs also have very little flutter over and above the measurement error.
Hey Max. Congratulations! I look forward to reading your regular contributions to BPro. And I hope you continue your summer tradition of a US visit for the PITCHf/x summit and multiple ball games. Best wishes.
I recall looking into this in the early days of PITCHf/x and concluding what RB just said: "a hanging curveball isn't necessarily a curveball with bad movement but with bad location."
Excellent analysis and writeup, Mike. At the 2010 summit, you and Matt Lentzner presented a study of how a pitcher's effectiveness depends on the direction the ball is moving as it crosses home plate. It is the same analysis that Matt wrote a ProGuestus about and that you linked to in your article (http://www.baseballprospectus.com/article.php?articleid=13273). So, here's my question: Now that you have HITf/x data, can you refine that earlier analysis by looking at how things like hSOB or the 12-deg projection of SOB (we need to invent a name for this) depends on the direction of the pitch? So the idea is that, rather than look at outcomes (such as BABIP), one could look instead at the characteristics of the batted ball. Might make for an interesting analysis.
Interesting observation. In some measurements we did a number of years ago, we found that elite slow-pitch softball players were routinely having bat speed in excess of 90 mph. If someone were to swing at an MLB pitch with that bat speed and made good contact, the ball would travel a very long distance--much farther than we probably have ever seen in MLB. My own benchmark for swing speed in MLB is about 70 mph, which is a lot less than achieved by these softball players. So, I am completely agreeing with what Matt is saying.
Actually a 2 mph increase in pitch speed will result in an ~0.4 mph increase in batted ball speed for a ball hit squarely on the sweet spot. Bat speed matters much more in determining batted ball speed.
One more comment on heyblue's post: the lightness of the ball will not affect the release speed. What matters is the mass (the "inertia") of the ball, not the weight. The mass is the same on the moon and earth, even though the weight is not.
Interesting about sinkerballs. If it were just reduced air density, then sinkerballs would sink *more*, not less. Most pitches, including sinkerballs, are thrown with backspin, which counteracts gravity. A sinkerball has less backspin than a normal fastball, so it has more "sink". But with essentially zero air density, it would sink even more. But normal fastball would sink as much. In fact, there would be the same movement on all pitches, with the movement determined by gravity alone. Of course, a sinkerball will actually sink less on the moon than on earth, since gravity is only 1/6 as strong.
Responding to heyblue: The fastball speed would not change on the moon, since the reported speed is the release speed. What will be different is the speed at home plate, which will be the same as the release speed. (OK, I know pitchf/x reports speed at 50 ft, not at release point; so the speed at 50 ft will be just a bit higher than on earth).
When it comes to insightful baseball analysis, you 'da man, Tango. But I'll look elsewhere for advice on women :).
My expectation would be that hitters benefit much more from reduced air resistance than pitchers. Witness the Coors Field effect. In that case, the reduced air resistance is due to altitude rather than temperature.
Another interesting thing to look at is the movement of the pitch (pfx_x,pfx_z) as a function of temperature. At higher temperatures, just as the lower air density reduces the drag, it also reduces the movement due to the spin. The difference in movement between Coors and the other stadiums is very clearcut from PITCHf/x data. The temperature effect would be more difficult to pull out but it might be worth a try.
Not to be too technical here, but it is not the drag coefficient that depends on temperature but the drag itself. Mike knows this and just said it wrong.
Now a question: What if you do the analysis using the release speed (i.e., at 50 ft) rather than the home plate speed. If you do this, do you see half of the temperature effect (based on your comment that the temperature dependence of the drag accounts for half of the observed effect)?
Great stuff, Matt!
Sorry...Mike beat me to it (and he actually remembered where the postings were).
Re andygarner: Lots of discussion about this last week over at THT (or perhaps at Tango's site, I forget now). What you really want are at least two (and preferably three) such devices, one located near home plate, one closer to the mound, and one in between.
Very nice article, Mike. Ike Hall's idea of using a "standard candle" to detect errors and possibly illuminate the way (: to a correction is an excellent one. As Mike knows, but most BPro readers may not, I have long advocated using drag coefficients (Cd) as another standard candle. Ike and I wrote an unpublished article about that in 2008 (http://webusers.npl.uiuc.edu/~a-nathan/pob/LiftDrag-1.pdf). The appealing thing about Cd values is that they really ought to be independent of both time and venue (once corrected for well-known atmospheric effects). So, Cd for a 95 mph fastball ought to be pretty much the same regardless of who/where/when. While this technique has proved to be excellent at identifying tracking errors, the goal of using that information to make corrections is a problem that still occupies me.
As promised, I have gone through my analysis again to tighten up the arguments and uncertainties for Coors and to do a real analysis of Chase. I should point out that my previous analysis of Chase was a little quick and dirty and the numbers I present now are really my best shot at the analysis for both venues. So, the final percent reductions in home runs are:
Coors: 27.5 +/- 4.3 %
Chase: 37.0 +/- 6.5 %
Some additional comments:
1. Re mgl: Interesting observation. So, here are some numbers for home runs/game for home and away:
So, there does seem to have been a 2nd change starting in 2005. There was a lot of blogging about that the time. I tried to find out whether there was some change in the parameters of the humidor had change in 2005, but no one I asked seems to know (or they're not telling). If I compare the 2005-2010 with the 1995-2001 numbers, there is a 32% reduction, which is getting embarrassingly close to my calculation (there is no reason to expect my calculation to be any better than the uncertainty I put on it).
2. Re tompschock: So, the speculation is that the Rockies stored balls at a lower humidity for the home team AB and higher for the away team. Of course, that is easy to check by simply pulling balls at random and measuring the COR. Frankly, I don't see how they could pull off that deception. Moreover, the consequences of getting caught would be far greater than I would suspect most MLB teams would be willing to risk. But I am expressing a highly uninformed opinion.
3. I spent most of the day Friday redoing the Chase analysis, since I only did it crudely for the article. I'll post something here in the next day or so about what I found.
Thanks to all of you who have commented favorably on my article. Let me briefly try to answer some of the questions.
1. In Lloyd Smith's laboratory experiments that I referred to, he carefully monitored the weight of the ball as a function of time. He found that it took many days for the weight to equilibrate. It is my understanding that the baseballs at Coors are removed from the humidor no more than a few hours before gametime. If such is the case, there would not be enough time for the water content of the ball to change in any significant way.
2. I want to think some more about Nailfan's question before attempting an answer.
3. I have hear the same anecdotal stories about the dry baseball feeling very slippery to the pitcher. Slippery means that there is less friction between the fingers and the ball, thereby inhibiting the ability of the pitcher to put spin on the ball. It would not be too difficult to measure the coefficient of friction of the surface of the ball as a function of relative humidity. No one has done that yet to my knowledge. It is much harder to relate that CoF to specific parameters of the pitched ball. If Arizona does decide to use a humidor, then we will have a wealth of pitchf/x data to make a before/after comparison of things like pitch movement.
4. I am glad that nateetan commented about the value of the HITf/x data to this analysis. I would go even further to say that the combination of HITf/x and hittracker is a very powerful analysis tool, since then we have both the initial velocity vector and the landing point/hang time. As I tried to emphasize in the article, that combination effectively determines the entire trajectory. Of course, that does limit us to studying only home runs. But it is better nothing (and much better than the type of landing point information we get from Gameday and other sources).
Congratulations, Colin, and best wishes.
Sorry to be so late jumping into this thread---busy week. Regarding release point, Colin remarks that the Pitchf/x convention is to give the release point at 50 ft. It is easily possible to use the full 9P fit to the trajectory to project back to 55 ft, which is closer to the actual release point. One can then compare FB with CB to see if the height at release is more consistent. Responding to Brian24: I think you misunderstand what Colin is saying regarding the break. The break is defined to be the deviation from a straight-line trajectory between 40 ft and the front edge of home plate (with gravity removed). So, it is not the movement in the first 10 ft but rather the movement in the last ~40 ft. Finally, regarding the differences between the CB and slider. A CB has topspin plus sidespin resulting in a glove-side break. A slider has only the sidespin (and perhaps a little backspin), but the spin axis is oriented forward, along the direction of flight. The component of spin in that direction does not contribute to the break. If the spin were fully aligned with the direction of motion, there would be no break at all (a gyroball). As a result, a slider has less total movement than other pitches, even though it is probably spinning just as fast.
The humidor has very little effect on the flight of a baseball, as researched and reported in this article:
It does have an effect on the bounce of a ball off the bat (http://webusers.npl.uiuc.edu/~a-nathan/pob/COR-humidity-kagan.pdf). I am not aware of any studies of the effect of humidity on the bounce off the ground. I suspect the time for de-humidifying is long compared to the length of a typical game. Overall, I am guessing that there is very little effect of the humidor on the bounce of the ball off the ground.
Line drives hit with backspin stay in the air longer due to the upward Magnus force. Opposite is true for line drives hit with topspin. The Magnus force is reduced in Colorado relative to other parks, for a given amount of spin. So, balls hit with backspin will fall faster and balls hit with topspin will fall slower than a comparably hit ball at sea level. Having said all that, I took a look at batted ball trajectories from some games last year. I think I can come up with a reasonable definition of line drive from the speed off bat and launch angle. I then look at the full trajectory and use a fitting procedure to estimate the spin on the ball. I find that line drives are predominantly hit with backspin. If such is the case, then I agree with the statement that line drives drop faster in Colorado than at sea level.
Sorry for being so wordy about this. Mostly it was a stream of consciousness exercise.
In my own analysis of hitf/x data from last year, I pretty much confirm what Brian says about how BABIP depends on the vertical launch angle. Based on analysis of nearly 15k batted balls, I find that if the speed off bat is larger than about 80 mph (a rather modest number), then BABIP peaks in the angular range 10-15 degrees, with BABIP exceeding 85%. If you actually look at the trajectory of a ball hit at 85 mph, 12.5 deg, it lands about 240 ft from home plate with a hang time of 2.6 sec, so falls in front of the outfielders with high probability. Also, it eludes the infielders, since it is too high for them to catch (it is about 18 ft high when about 100 ft from home plate). The maximum height is a bit larger, ~20 ft. Whether you call it a line drive or something else is a matter of semantics. It is a very well-hit ball. If you look at home runs, then the home run probability peaks with a launch angle in the 25-35 deg range.
The message seems to be pretty clear, at least to me. If you want to get on base (as opposed to hit a home run), keep the launch angle low.
Unfortunately, there is not enough data that has been released to look at these numbers in a statistically meaningful way for specific hitters.
Readers may be interested in the early-season analysis I did of how ball parks differ in the carry of a fly ball. The analysis combined hitf/x data for the initial trajectory with hittracker data (thanks to Greg R.) for the landing point and flight time. See my writeup at
Brian: regarding the 400 ms, here is something I posted yesterday over at THT:
Here is an analysis that might interest you. Suppose we agree that 0.400 sec is the minimum amount of time needed for a pitcher to react. Suppose also that we will ban all bats that are capable of hitting a ball that has a shorter flight time to the pitcher than 0.400 sec. What maximum speed off bat does that imply? How far would such a ball travel if hit at a typical home run launch angle (30 deg). Here is the answer (I assume 53.3 ft flight distance from contact to pitcher):
Speed off bat: 95 mph
Home run distance: 356 ft
So, by banning all bats capable of hitting a baseball so that the flight time to the pitcher is less than 400 ms, we would reduce fly ball distances to less than 356 ft. That would drastically change the game at the high school and college level. I suspect most wood bats would be banned by this criterion.
I think it was 70 mph, since that is what the NCAA was using in their bat testing. However, for purposes of comparing one bat to another, the exact value of the pitch speed is not so important, as long as it is the same for the two bats you are comparing.
My web site has lots of info and links:
Note particularly the link to Dan Russell's site:
Sorry for being so late to get back to this thread. In case anyone is still watching, here is a response to kantsipr's questions:
48.000 is European for 48,000, so it really is 48 kHz. The radar is continuous at a frequency of about 10 GHz. The sampling rate in their data acquisition is 48 kHz.
The spin rate is not determined by the broadening of the Doppler-shifted signal, although that was what I originally thought also. The reflected signal is modulated by the spin frequency due to the fact that the reflectivity of the radar signal is not uniform over the full surface of the ball (more reflection from the stitches than from the white part). This results in "sidebands" in the frequency spectrum, separated from the main peak by the spin rate.
The spin axis is not directly determined from the signal. It is inferred from the reconstructed trajectory (just as it is in pitchf/x).
I am late joining this thread since I had long ago let me subscription expire. Now that it is renewed, I have a few comments.
Regarding the "less speed drop" with a sinker or cutter, I am guessing that it has to do with the spin dependence of the drag, with a higher spin giving a larger drag (and more speed loss). The same information is indirectly available with Pitchf/x (spin is not measured but the effect of spin--the pfx values--is measured). In fact, Dan Fox noted in a BP article two years ago the correlation between spin (as determined in the manner I said) and speed loss. I have done a similar analysis of more recent data and reach the same conclusion that when the spin is higher, the speed loss is also higher (on the average).
Memo to Joe Lefko: Presenting your numbers to 20 (or whatever) significant digits is not credible (I am sure you know this). Better not to show more figures than the precision of the data dictates.
Re Fredrik Tuxen: Yes, it would be good to have him interviewed for BP. And it would be good to hear what he thinks are the differences between TrackMan and Pitchf/x with regard to pitched baseballs.
Just my own brief commment: Getting 48000 samples per second (vs. 60 samples/second in each of two cameras for Pitchf/x) does not necessarily mean that the inferred trajectory is better. The laws of physics (which I am sworn to obey!) tell us that the trajectory has to be fairly smooth and you don't need thousands of points to determine it. It can't hurt having all the data TrackMan provides--it just doesn't help either.
And finally: The Fox Trax box on the right of the screen comes from Pitchf/x, not from TrackMan. The latter is used only for Fox Trax + (initial and final speed and flight time).